A variety of common electronic circuits such as power supplies, rechargeable battery controllers and chargers, electric motor drivers, LED drivers, etc., usually contain one or more low-ohmic resistors for current sensing.
Overwhelming majority of commonly used resistors is based on a two-terminal design. Reference is now made to FIG. 1 (prior art), which illustrates by way of example, two-terminal resistor 10. Current I, that is monitored and has to be measured, is forced across resistor terminals 12 and resistive element 14. Voltage V, measured by voltmeter 90, is directly proportional to current I and is sensed across terminals 12.
Terminals 12 and resistive element 14 are electrically connected in series and form compound resistor 10 having resistance R and TCR α. Parameters R and α are expressed as functions of resistance Re and TCR αe of resistive element 14, and resistance Rt and TCR αt of terminals 12. Parameters R and α are then computed as follows:
                              R          =                                    R              e                        +                          R              t                                      ;                            (        1        )                                          α          =                                                                      α                  e                                ⁢                                  R                  e                                            +                                                α                  t                                ⁢                                  R                  t                                                                                    R                e                            +                              R                t                                                    ,                            (        2        )            
Commonly, resistance Re of resistive element 14 is several orders of magnitude higher than resistance Rt of terminals 12. It follows from equations (1) and (2) that in such a case, resistance R and TCR α of resistor 10 are pre-determined by resistance Re and TCR αe of resistive element 14, respectively: R≈Re; α≈αe.
In a low-ohmic film chip resistor, the nominal resistance value may have the same order of magnitude as the resistance of the terminals. Resistance of the film terminals may reach 2 milliohms (1 milliohm per each terminal). The TCR of the materials that form a film terminal (for example copper, silver, nickel, tin) is about +4·103 ppm/K.
The share of terminal resistance Rt, in total resistance R, can be calculated as in the following example:
given a film resistor with a resistive element that is characterized by 10 milliohm resistance and 30 ppm/K TCR;
if the total resistance of the terminals is 2 milliohms (typical for film resistor), the share of terminal resistance Rt, in total resistance R (per equation (1)) is:
            2              (                  10          +          2                )              *    100    ⁢    %    ≈      16.7    ⁢          %      .      This number characterizes the maximum value of the resistance R uncertainty. The resistance R uncertainty becomes apparent, for example, when a resistor is tested while the position of contact probes on terminals varies. The TCR of the total resistor calculated per (2) is as high as 692 ppm/K. That is why the manufacturing of two-terminal film resistors with a tolerance better than 5% and a TCR better than 600 ppm/K is impossible for 10 milliohm nominal resistance value and below.
One way to significantly reduce the influence of the resistance and TCR of terminals on resistance and TCR of low-ohmic resistor is by using a design based on a four-terminal measurement technique, called Kelvin sensing. Reference is now made to FIG. 2 (prior art), which illustrates by way of example, four-terminal resistor 15.
The essence of four-terminal resistor 15 is in using two separate pairs of terminals:                (a) current carrying (“Force”) terminals 12; and        (b) voltage measurement (“Sense”) terminals 16, which are connected directly to the resistive element 14.The resistance of four-terminal resistor 15 (ratio of “Sense” voltage to current I forced across “Force” terminals 12) is substantially independent of testing and mounting conditions.        
The TCR of conventional four-terminal resistors, for example, the thick-film four-terminal current sensing resistor provided by European patent EP 1,473,741, given to Carl Berlin et al, are commonly no better than the TCR of the utilized resistive element material. Further improvement of the thermal stability of resistors is associated with adjustment of the TCR of the resistive element, in the manufacturing process of the resistors. The following are prior art methods to control (adjust) the TCR of a resistor during the manufacturing process:                a) Compensating for intrinsic TCR of the resistive element material in resistive elements made from metal foil. Mismatch of temperature coefficients of expansion (TCE) that characterize foil and the ceramic substrate that the foil is glued to, causes stress and strain in the foil, which are transformed into electrical resistance change (piezoresistive effect).                    The compensation method used in precision foil resistors, as described for example in U.S. Pat. No. 3,405,381, given to Felix Zandman et al., brings the resistance change down to sub-ppm/K levels. The method relies on proper selection (preparation) of raw materials and not on TCR adjustment in the resistor assembly process.                        b) Manufacturing the resistive element using a special material that when treated by heat changes the physical properties. For example, in thin-film technology, it is possible to precisely adjust by heat treatment the TCR of thin resistive films down to several ppm/K. Unfortunately, for economical reasons, minimal resistance of thin-film resistors cannot be extended far below 1 Ohm, which is common for current sense resistors.        c) Manufacturing the resistive element using special manufacturing processes and materials that make it possible to change the physical properties of the resistive material by applying local heat directly on the component substrate. For example, U.S. Pat. No. 4,703,557, given to John Nespor et al., proposes to pre-fire thick film resistor in a kiln, to provide an initial TCR adjustment. Then, the resistor is laser annealed to controllably adjust the TCR. The process requires scanning of the entire resistor surface by a laser beam and thereby the process is expensive (time inefficient). Another method is proposed by US Patent Application 20060279349 “Trimming temperature coefficients of electronic components and circuits”. The essence of the method is to form both the resistor and the heater on a silicon substrate. Special circuitry activates the heater resulting in TCR adjustment of the resistor. However, this solution is not suitable for resistors dissipating power more than 1 milliwatt during normal use, because self-heating may change the previously adjusted TCR. Typical current sense resistors dissipate hundreds of milliwatts of power. Therefore, the described method is not suitable for current sensors.        d) Forming a four-terminal resistor by cutting slots in the terminals of the resistor. Reference is made to FIG. 3 (prior art), which is a perspective view of four-terminal resistor 20, such as described in U.S. Pat. No. 5,999,085, given to Joseph Szwarc. Resistor 20 includes metal terminals 22 and metal resistive element 24. Slots 25 divide each terminal 22 to current pad portion 26 and sense pad portion 28. The depth of slots 25 influences the TCR of four-terminal resistor 20 and is selected to optimize the thermal stability of resistor 20. The method is empirical and suitable for resistors having solid metal terminals.                    Wraparound film terminals in film resistors are typically deposited on ceramic substrate and the cutting through the terminals during the manufacturing process is questionable.                        e) Using two resistive elements connected in parallel or two resistive elements connected in series, for example as described in U.S. Pat. No. 3,970,983, given to Isao Hayasaka, and in U.S. Pat. No. 6,097,276, given to Jan Van Den Broek at al. Reference is made to FIG. 4 (prior art), which is a perspective view of two-terminal resistor 30, having two resistive elements 34 electrically connected in parallel, disposed on substrate 36. Reference is also made to FIG. 5 (prior art), which is a perspective view of two-terminal resistor 40, having two resistive elements 44 electrically interconnected in series by conductive element 48 and disposed on substrate 46. One of resistive elements (34, 44) in each pair has a positive TCR, and the second resistive element has a negative TCR. Laser trimming of both resistive elements makes it possible to adjust both resistance and TCR of the compound resistor (30, 40). It is not possible to implement the method with resistive materials having only positive (only negative) TCR. Up-to-date, low resistance thick-film materials, based on noble metals, have only positive TCR.        
There is therefore a need and it would be advantageous to be able to design four-terminal current sense resistors with a TCR adjustment procedure, applicable in a manufacturing process. It would be advantageous to be able to enable TCR adjustment while using resistive materials with only positive (or only negative) TCR.